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A.I. gratefully acknowledges the financial support of The Faculty of Science and Technology at Aarhus University through a Sabbatical scholarship and the hospitality of the Quantum Technology group, the Centre for Theoretical Atomic, Molecular and Optical Physics and the School of Mathematics and Physics, during his stay at Queen’s University Belfast. A.B. acknowledges the hospitality of the Institute for Theoretical Physics and the “Nonequilibrium quantum dynamics” group at Universität Stuttgart, where part of this work was carried out. R.P. and M.P. acknowledge the support by the SFI-DfE Investigator Programme (Grant No. 15/IA/2864) the Eropean Union’s Horizon 2020 FET-Open project SuperQuLAN (899354) and TEQ (766900). M.P. acknowledges support by the Leverhulme Trust Research Project Grant UltraQuTe (Grant No. RGP-2018-266), the Royal Society Wolfson Fellowship (RSWF/R3/183013), the UK EPSRC (Grant No. EP/T028424/1) and the Department for the Economy Northern Ireland under the US-Ireland R&D Partnership Programme. A.B. also acknowledges support from H2020 through the MSCA IF pERFEcTO (Grant Agreement No. nr. 795782) and from the DeutscheForschungsgemeinschaft (DFG, German Research Foundation) Project No. BR5221/4-1. We consider a finite one-dimensional chain of quantum rotors interacting with a set of thermal baths at different temperatures. When the interaction between the rotors is made chiral, such a system behaves as an autonomous thermal motor, converting heat currents into non-vanishing rotational ones. Such a dynamical response is strongly pronounced in the range of the Hamiltonian parameters for which the ground state of the system in the thermodynamic limit exhibits a quantum phase transition. Such working points are associated with large quantum coherence and multipartite quantum correlations within the state of the system. This suggests that the optimal operating regime of such quantum autonomous motor is one of maximal quantumness. 9 pages, 9 figures Peer reviewed

In this article, we prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case.

Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts often grossly wrong, concerning the numbers of people who get infected or die? The purpose of this study is to better understand the stochastic nature of an epidemic disease, and answer the above questions. Much of the work on infectious diseases has been based on "SIR deterministic models," (Kermack and McKendrick:1927.) We will explore stochastic models that can capture the essence of the seemingly erratic behavior of an infectious disease. A stochastic model, in its formulation, takes into account the random nature of an infectious disease. The stochastic model we study here is based on the "birth-and-death process with immigration" (BDI for short), which was proposed in the study of population growth or extinction of some biological species. The BDI process model ,however, has not been investigated by the epidemiology community. The BDI process is one of a few birth-and-death processes, which we can solve analytically. Its time-dependent probability distribution function is a "negative binomial distribution" with its parameter $r$ less than $1$. The "coefficient of variation" of the process is larger than $\sqrt{1/r} > 1$. Furthermore, it has a long tail like the zeta distribution. These properties explain why infection patterns exhibit enormously large variations. The number of infected predicted by a deterministic model is much greater than the median of the distribution. This explains why any forecast based on a deterministic model will fail more often than not. 28 pages, 14 figures

We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such L2 ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis. We characterize such systems completely as appropriately weighted Fourier transforms of orthogonal polynomials and present a number of illustrative examples, inclusive of a Sobolev‐orthogonal system whose leading N coefficients can be computed in O ( N log N ) $ \mathcal{O} (N\log N)$ operations. Funder: Narodowe Centrum Nauki; Id: http://dx.doi.org/10.13039/501100004281 Funder: Simons Foundation; Id: http://dx.doi.org/10.13039/100000893

In this paper, a class of holomorphic invariant metrics are introduced on the irreducible classical domains of type I-IV , which by their very definitions are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio [2]. These metrics are of particular interesting since they are holomorphic invariant non-Hermitian quadratic complex Finsler metrics found so far in literature which enjoy good regularity as well as convexity and can be explicitly expressed so as to admit differential geometric studies. These metrics are explicitly constructed via deformations of the corresponding Bergman metrics on the irreducible classical domains and they are all proved to be complete K\"ahler-Berwald metrics. Moreover, these metrics enjoy very similar curvature properties as that of the Bergman metrics on the irreducible classical domains, namely they all have negative holomorphic sectional curvatures and non-positive holomorphic bisectional curvatures. From the view point of complex analysis, these metrics are analogue of Bergman metrics in complex Finsler geometry without Hermitian quadratic restrictions in the philosophy of S. S. Chern [8]; furthermore, they are all K\"ahler Finsler-Einstein metrics in the sense of T. Aikou [5].

We report on the changing-look nature of the active galactic nucleus (AGN) in the galaxy NGC 4156, as serendipitously discovered thanks to data acquired in 2019 at the Telescopio Nazionale Galileo (TNG) during a students' observing programme. Previous optical spectra had never shown any signatures of broad-line emission, and evidence of the AGN had come only from X-ray observations, being the optical narrow-line flux ratios unable to unambiguously denote this galaxy as a Seyfert. Our 2019 TNG data unexpectedly revealed the appearance of broad-line components in both the H$\alpha$ and H$\beta$ profiles, along with a rise of the continuum, thus implying a changing-look AGN transitioning from a type 2 (no broad-line emission) towards a (nearly) type 1. The broad-line emission has then been confirmed by our 2022 follow-up observations, whereas the rising continuum has no longer been detected, which hints at a further evolution backwards to a (nearly) type 2. The presence of broad-line components also allowed us to obtain the first single-epoch estimate of the black hole mass (log(MBH/Msun) $\sim$ 8.1) in this source. The observed spectral variability might be the result of a change in the accretion activity of NGC 4156, although variable absorption cannot be completely excluded. Comment: 9 pages, 6 figures. Accepted for publication in A&A Letters

We perform a statistical analysis of deterministic energy-decreasing algorithms on mean-field spin models with complex energy landscape like the Sine model and the Sherrington Kirkpatrick model. We specifically address the following question: in the search of low energy configurations is it convenient (and in which sense) a quick decrease along the gradient (greedy dynamics) or a slow decrease close to the level curves (reluctant dynamics)? Average time and wideness of the attraction basins are introduced for each algorithm together with an interpolation among the two and experimental results are presented for different system sizes. We found that while the reluctant algorithm performs better for a fixed number of trials, the two algorithms become basically equivalent for a given elapsed time due to the fact that the greedy has a shorter relaxation time which scales linearly with the system size compared to a quadratic dependence for the reluctant. Comment: 20 pages, 6 figures. New version, to appear on J.Phys.A

The possibility of obtaining an open set of regular cosmological models is discussed. Cylindrical stiff perfect fluid cosmologies are studied in detail. The condition for geodesic completeness is easy to check. A large family of non-singular models is found therein. 4 pp. Proceedings of ERE 2002, Ma\'o, Spain

Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. It is usually formulated as a constrained optimization problem and optimized via a modified version of gradient descent. In this work, by interpreting the continuous parameters (unconstrained) as the dual of the quantized ones, we introduce a Mirror Descent (MD) framework for NN quantization. Specifically, we provide conditions on the projections (i.e., mapping from continuous to quantized ones) which would enable us to derive valid mirror maps and in turn the respective MD updates. Furthermore, we present a numerically stable implementation of MD that requires storing an additional set of auxiliary variables (unconstrained), and show that it is strikingly analogous to the Straight Through Estimator (STE) based method which is typically viewed as a "trick" to avoid vanishing gradients issue. Our experiments on CIFAR-10/100, TinyImageNet, and ImageNet classification datasets with VGG-16, ResNet-18, and MobileNetV2 architectures show that our MD variants obtain quantized networks with state-of-the-art performance. Code is available at https://github.com/kartikgupta-at-anu/md-bnn. Comment: This paper was accepted at AISTATS 2021

An important concern in the application of gamma-ray bursts (GRBs) to cosmology is that the calibration of GRB luminosity/energy relations depends on the cosmological model, due to the lack of a sufficient low-redshift GRB sample. In this paper, we present a new method to calibrate GRB relations in a cosmology-independent way. Since objects at the same redshift should have the same luminosity distance and since the distance moduli of Type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a GRB at a given redshift by interpolating from the Hubble diagram of SNe Ia. Then we calibrate seven GRB relations without assuming a particular cosmological model and construct a GRB Hubble diagram to constrain cosmological parameters. From the 42 GRBs at $1.4